Co-symplectic geometry and co-Lagrangian subspaces

A new natural structure on the tangent spaces of a co-tangent bundle is introduced and some of its properties are investigated. This structure is based on a symmetric bilinear form and leads to a geometry that is, in many respects, analogous to the symplectic geometry. The new structure can thus justifiably be called co-symplectic geometry. The null structure of co-symplectic vector spaces is investigated in detail. It is found that the manifold of all maximally isotropic subspaces of a co-symplectic vector space is a homogeneous compact manifold of dimension 1/2n(n–1) consisting of two diffeomorphic components and having fundamental groupZ ₂Z ₂. A representation of the fundamental group of this manifold is explicitly constructed in terms of quadrupoles of co-Lagrangian subspaces.     

基于双模相干-纠缠态表象的算符恒等式构造法

利用最近引进的相干-纠缠态|x,α〉表象和有序算符内的积分技术,给出了关于双模光场正交分量（X₁+X₂）/2^1/2和参数化的正交分量（μX₁+νX₂）/λ的函数的若干正规乘积展开式,这对于研究场的高阶压缩行为和构建广义压缩态是有用的. 关键词： 双模相干-纠缠态 算符恒等式 有序算符内的积分技术     

Gerbes over Orbifolds and Twisted K-Theory

In this paper we construct an explicit geometric model for the group of gerbes over an orbifold X. We show how from its curvature we can obtain its characteristic class in H³(X) via Chern-Weil theory. For an arbitrary gerbe , a twisting K_orb(X) of the orbifold K-theory of X is constructed, and shown to generalize previous twisting by Rosenberg [28], Witten [35], Atiyah-Segal [2] and Bowknegt et. al. [4] in the smooth case and by Adem-Ruan [1] for discrete torsion on an orbifold.The first author was partially supported by the National Science Foundation and Conacyt-México     

Nuclear magnetic double resonance for a spin system subject to scalar relaxation of the second kind

The equation of motion of a reduced spin density operator characterizing the state of a group of spins scalar coupled to a second group of spins which are either relaxing rapidly and/or irradiated with a strong radiofrequency field is derived within the framework of the non-viscous liquid approximation. An analytic expression for the spectral densities entering this equation is derived within the extreme narrowing approximation for the case in which the relaxation rates of the nuclei in the second group of spins are much greater than any scalar couplings between them. The resultant equation is used to discuss the conditions needed in a high resolution nuclear magnetic double resonance experiment to decouple a spin-½ nucleus (A) from a rapidly relaxing quadrupolar nucleus (X) in the fast relaxation limit, defined by |2πJ_AX T _1X | ? 1, in which the A resonance consists of a single broadened line. It is found that, if (ω _A - ω _X )² ? T _1X ^-2 so that the x and y components of the J_AX coupling can be neglected, decoupling, in the sense that all broadening of the A resonance is removed, occurs only when the strength of the B ₂ field be such that γ _X ² B ₂ ² ? T _1X ^-2 and that the conventional decoupling criterion γ _X ² B ₂ ² ? 4π² J_AX ² is not applicable. However, if the x and y components of the A-X scalar coupling cannot be neglected because the condition (ω _A - ω _X )² ? T _1X ^-2 is not satisfied, it is found that the X spin can never be entirely decoupled. It is shown that such double resonance experiments enable both the coupling constants between spin-½ and quadrupolar nuclei and the relaxation times of the latter nuclei to be extracted in situations in which measurement of the half-widths of spin-1/2 transitions can only yield the product J_AX ² T _1X in the absence of irradiation of the quadrupolar nuclei.     

Rightfulness of Summation Cut-Offs in the Albedo Problem with Gaussian Fluctuations of the Density of Scatterers

The one-dimensional version of the radiative transfer problem (i.e. the so-called rod model) is analysed with a Gaussian random extinction function (x). Then the optical length X = ₀ ^Ldx(x) is a Gaussian random variable. The transmission and reflection coefficients, T(X) and R(X), are taken as infinite series. When these series (and also when the series representing T ²(X), T ²(X), R(X)T(X), etc.) are averaged, term by term, according to the Gaussian statistics, the series become divergent after averaging. As it was shown in a former paper by the authors (in Acta Physica Slovaca (2003)), a rectification can be managed when a `modified' Gaussian probability density function is used, equal to zero for X > 0 and proportional to the standard Gaussian probability density for X > 0. In the present paper, the authors put forward an alternative, showing that if the m.s.r. of X is sufficiently small in comparison with , the standard Gaussian averaging is well functional provided that the summation in the series representing the variable T ^m-j (X)R ^j (X) (m = 1,2,..., j = 1,...,m) is truncated at a well-chosen finite term. The authors exemplify their analysis by some numerical calculations.     

The L p Spectrum of Locally Symmetric Spaces with Small Fundamental Group

We determine the L ^p spectrum of the Laplace-Beltrami operator on certain complete locally symmetric spaces M whose universal covering X is a symmetric space of non-compact type with rank one. More precisely, we show that the L ^p spectra of M and X coincide if the fundamental group of M is small and if the injectivity radius of M is bounded away from zero. In the L ² case, the restriction on the injectivity radius is not needed.      

分子XH(X=O,S, Se和 Te)中的正电子能级与正电子原子

基于全对称群的Dirac方程, 研究当存在核场时的正电子能级及其与核场的关系, 即计算在分子OH, SH, SeH和 TeH的核场下的正电子能级. 这时正电子的能量约为 e⁺=-1.022 MeV. 对于低能级, 当核场强增大时, 其能量有所升高, 而对较高能级, 核场强增大时, 其能量无明显变化. 正负电子的湮没过程为三光子湮没过程(the three-photon annihilation). 而当生成e⁺- e^-< 关键词： Dirac方程 三光子湮没过程 正态的正电子原子 电荷宇称守衡     

Stability of Charged Exciton States in Quantum Wires

We show that the order of energies of negative (X⁻) and positive (X⁺) trions in quantum wires is determined by the relative electron and hole lateral confinements. For equal electron and hole confinement, X⁺ has a larger binding energy, but a small imbalance towards a stronger hole localization changes the order of the X⁻ and X⁺ recombination lines in the photoluminescence spectrum.     

Nonlinear Markov Semigroups and Interacting Lévy Type Processes

Semigroups of positivity preserving linear operators on measures of a measurable space X describe the evolutions of probability distributions of Markov processes on X. Their dual semigroups of positivity preserving linear operators on the space of measurable bounded functions B(X) on X describe the evolutions of averages over the trajectories of these Markov processes. In this paper we introduce and study the general class of semigroups of non-linear positivity preserving transformations on measures that is non-linear Markov or Feller semigroups. An explicit structure of generators of such groups is given in case when X is the Euclidean space R ^d (or more generally, a manifold) showing how these semigroups arise from the general kinetic equations of statistical mechanics and evolutionary biology that describe the dynamic law of large numbers for Markov models of interacting particles. Well posedness results for these equations are given together with applications to interacting particles: dynamic law of large numbers and central limit theorem, the latter being new already for the standard coagulation-fragmentation models.     

Realizability of Point Processes

There are various situations in which it is natural to ask whether a given collection of k functions, ρ _j (r ₁,…,r _j ), j=1,…,k, defined on a set X, are the first k correlation functions of a point process on X. Here we describe some necessary and sufficient conditions on the ρ _j ’s for this to be true. Our primary examples are X=ℝ ^d , X=ℤ ^d , and X an arbitrary finite set. In particular, we extend a result by Ambartzumian and Sukiasian showing realizability at sufficiently small densities ρ ₁(r). Typically if any realizing process exists there will be many (even an uncountable number); in this case we prove, when X is a finite set, the existence of a realizing Gibbs measure with k body potentials which maximizes the entropy among all realizing measures. We also investigate in detail a simple example in which a uniform density ρ and translation invariant ρ ₂ are specified on ℤ; there is a gap between our best upper bound on possible values of ρ and the largest ρ for which realizability can be established.     

The Representation of Isometric Operators on <Emphasis Type="Italic">C</Emphasis><Superscript>(1)</Superscript>(<Emphasis Type="Italic">X</Emphasis>)

In this paper,we introduce a new norm on C ⁽¹⁾(X), which is induced by a hexagon on R ², and prove that every isometric operator on C ⁽¹⁾(X) can be induced by a homeomorphism of X, where X is a connected subset of R.     

General covariant energy-momentum conservation law in general spacetime

We discuss the conservation laws in general spacetime with torsion and nonmetricity by use of the Noether theorem. We give a general Lagrangian density, which can be reduced to the one given by Rauch and Nieh (1981). The general covariant energy-momentum conservation law is obtained with respect to the general displacement transformationX ^' =X +e _a b ^b , which is a special case of general conservation laws. It is shown that in such a case, the existence of superpotentials is assured. The results are the natural extension of references [1,2].     

A Note on Universality of the Distribution of the Largest Eigenvalues in Certain Sample Covariance Matrices

Recently Johansson and Johnstone proved that the distribution of the (properly rescaled) largest principal component of the complex (real) Wishart matrix X*X(X ^t X) converges to the Tracy–Widom law as n,p (the dimensions of X) tend to in some ratio n/p>0. We extend these results in two directions. First of all, we prove that the joint distribution of the first, second, third, etc. eigenvalues of a Wishart matrix converges (after a proper rescaling) to the Tracy–Widom distribution. Second of all, we explain how the combinatorial machinery developed for Wigner random matrices in refs. 27, 38, and 39 allows to extend the results by Johansson and Johnstone to the case of X with non-Gaussian entries, provided n–p=O(p ^1/3). We also prove that _max(n ^1/2+p ^1/2)²+O(p ^1/2 log(p)) (a.e.) for general >0.     

Correct bound states of the non- linear oscillator through non-variational method: Failure of the variational method

A method for obtaining correct bound states of the non-linear oscillatorH = P ²+X ² +X ²(X ²) is described. It is shown that the variational method fails to yield correct ground state energy.     

Magnetic orientation of carbon nanotubes at temperatures of 231 K and 314 K

Carbon nanotubes were placed in magnetic fields of  80.0 kOe at temperatures of 231 K and 314 K. Scanning electron microscopy showed that nanotubes were oriented with the tube axis parallel to the fields. It was also observed that the probability of the orientation became higher, when the temperature was raised from 231 K to 314 K. The anisotropy in the susceptibilities parallel X∥ and perpendicular X _⊥ to the tube axis is suggested to increase with rise in temperature: X∥ ? X⊥ = (4 ± 2) × 10^?6 emu mol^?1 (per mol of carbon atoms) at 231 K and X∥ ? X⊥ = (45 ± 27) × 10^?6 emu mol^?1 at 314 K.     

The Ground StateXΣof NaK Revisited

Laser-induced fluorescence (LIF) optical spectra of theD¹Π–X¹Σ⁺system of the NaK molecule have been reinvestigated. In this new analysis, quantum numbers have been assigned to 3000 selected fluorescence lines for a wide range of vibrational and rotational levels (J≤ 149,v′ ≤ 23,v″ ≤ 47). A new set of constants of theX¹Σ state (Dunham-type coefficients) and term values of theD¹Π state have been determined by a weighted least-squares fit of the LIF optical lines of theD–Xsystem, some lines of theC–Xsystem, and microwave spectral data reported recently. Constants forX¹Σ (in cm⁻¹) are as follows: ω_e= 123.993, ω_ex_e= 0.3045,B_e= 0.095229, and α_e= 4.48 × 10⁻⁴. The equilibrium internuclear distance isr_e= 3.49903 Å, very little changed from the microwave value.     

Electronic emission spectra ofo- andm-fluorobenzaldehyde vapours

The high resolutionnπ* electronic emission spectra ofo- andm-fluoro-benzaldehyde vapours in the region 365–560 nm excited in a discharge are reported for the first time. The spectra of both the compounds consist of theA ¹ A″ -X ¹ A′ fluorescence as well as thea ³ A″ -X ¹ A′ phosphorescence bands. In the case ofo-isomer, all the eleven out-of-plane vibrations have been observed in the fluorescence and the phosphorescence, though weakly in the latter, whereas in the case ofm-isomer, only ten have been observed in the fluorescence and nine in the phosphorescence. It is found that the most intense bands in both the fluorescence and the phosphorescence spectra of these molecules belong to the trans-O rotamer.     

用代数-能量自洽法研究双原子分子解析势能函数

基于计算双原子分子完全振动能谱及离解能的代数方法 (algebraic method,AM)和研究双原子分子解析势能函数的能量自洽法(energy consistent method,ECM),建立了计算双核分子体系精确解析势能函数的代数-能量自洽法(AM-ECM).应用AM-ECM方法研究了7Li+2-23Σg,KH-X1Σ+,NaLi-X1Σ+和NaLi-A1Σ+电子态的解析势能表达形式,并与其他方法的研究结果进行了比较,获得了能正确描述这些电子态在渐近区和离解区的精确解析表达结果.     

A Model Independent Method of the X° (960) Meson Spin Parity Determination

To establish the X→ (960) meson spin parity it is suggested to study the correlation between the production process K^?He⁴ → X⁰ ΔH⁴ and the decay process X⁰ → η²π.     

Productions of X(1835) as baryonium with sizable gluon content

X(1835) has been treated as a baryonium with sizable gluon content, and to be almost flavor singlet. This picture allows us to rationally understand X(1835) production in J/ψ radiative decays, and its large couplings with pˉ, η^′ππ. The processes ϒ(1S) → γX(1835) and J/ψ → ωX(1835) have been examined. It has been found that Br(ϒ(1S) → γX(1835))Br(X(1835) → pˉ) < 6.45×10^-7, which is compatible with CLEO's recent experimental result (Phys. Rev. D 73, 032001 (2006) hep-ex/0510015). The branching fractions Br(J/ψ → ωX(1835)), Br(J/ψ → ρX(1835)) with X(1835) → pˉ and X(1835) → η^′π⁺π^- have been estimated by the quark-pair creation model. We show that they are heavily suppressed, so the signal of X(1835) is very difficult, if not impossible, to be observed in these processes. The experimental checks for these estimations are expected. The existence of the baryonium nonet is conjectured, and a model-independent derivation of their production branching fractions is presented.